Can I Use a Religious Term for A Game Title (bearing in mind it WON'T be used for commercial use)?

Actually, the hymn is "Ave Maria," or "Hail, Mary." You can use that for anything. I don't find it particularly sacrilegious, any more so than calling a desperation p a "Hail, Mary." However, "Ave Mary A" is a song title by Pink, as you know, and that is probably subject to copyright. That really wouldn't affect you in a noncommerical setting, but I might want to avoid it, anyway.